The British pair will play together in Sunday's concluding round after Sullivan's 68 gave the 28-year-old an aggregate score of 200 to McIlroy's 201 at the European Tour's season finale.
American Patrick Reed (68) is on 203, while Argentina's Emiliano Grillo (71) and Korea's Byeong-hun An (66) are both a further stroke behind.
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"I'm very satisfied. I hit the ball fantastically well from tee to green," McIlroy, 26, told reporters.
"Everything was just firing today and that's why I'm walking off the course a little bit disappointed because that 65 could have easily been a 62 or a 61. But it's still a great position going into tomorrow."
Sullivan had begun the day on 12-under, one stroke ahead of Grillo and four clear of the world number three McIlroy.
That meant Sullivan was last to tee off. McIlroy started two groups ahead of him and the Northern Irishman exerted some immediate pressure, making a 10-foot birdie on the first and picking up further shots at holes two and four.
Sullivan, famed for playing with a smile, looked serious on the first tee as he waited to start.
Course conditions were tough and the only respite from the sweltering heat was a sporadic, swirling, blustery wind.
Sullivan sunk a three-foot birdie on the second hole, but fluffed the chance to pick up another stroke at the third, missing from 10 feet.
England's Andy Sullivan applauds his fan club at the eighteenth green at the end of the third round.
Image credit: Reuters
Worse was to follow on four when a simple putt lipped out for a bogey as McIlroy's charge seemed to inhibit the usually ebullient Englishman.
Yet an eight-foot birdie at five and another on seven put Sullivan ahead again.
"I just didn't feel like I was hitting it as close as I was yesterday," Sullivan told reporters. "It was windy. I found it quite tough to actually get the ball the right distance."
McIlroy was often sublime, picking up further shots at seven and 10, while the four-time major winner followed a bogey on 12 with three successive birdies.
Sullivan was unbowed, however, also birdying 15. He picked up another shot on 17 with a 20-footer that had him cupping his ears to acknowledge the roar of his boisterous fans, the self-proclaimed Sully Army.
McIlroy erred on the 18th, rolling a simple birdie chance wide, while Sullivan puffed out his cheeks in relief after later making a tricky par putt on the same green.
"If I keep putting the way I am and hitting the ball well, I can still do it," added Sullivan.
"Rory will have his own fans out there, probably 90 percent of them, but my boys make a lot of noise. I felt like the putter really saved me the last few holes."
As well as seeking a third tour win of the season, McIlroy is eyeing a third Race to Dubai title in four years, the prize awarded to Europe's biggest money earner.
McIlroy led going into the season climax and of the six other golfers who could potentially usurp him, only Danny Willett still stands a chance with 18 holes to play.
The Englishman's third-round 67 puts him on 205, four adrift of McIlroy.
"I'd love to finish the year on a high and win the Race to Dubai and more importantly win this tournament," McIlroy said.
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